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Critical limit
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How can we decide if any particular measurement near zero is actually zero or represents a true positive count?

There must be some level above which we can be confident, to a degree, that a net count is valid. This is the critical limit, LC.

If we have a count, A, then when

A > ka s0,

the count is statistically significant
and when

A ka s0,

the count is not significant, where s0 is the standard deviation of the distribution and the factor ka is selected so as to provide a predetermined degree of confidence in the solution.

When ka corresponds to the 95% confidence level

LC = 2.33 s

where s is the standard deviance of background estimate (counts).

Definition of critical limit, LC.
(The vertical axis represents the frequency of observing a particular count)

 

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1999, 2000 The University of Liverpool, Department of Physics

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